1. Field of the Invention
The present invention relates to an apparatus for controlling the air-fuel ratio of an internal combustion engine.
2. Description of the Related Art
Generally, catalytic converters such as three-way catalytic converters are disposed in the exhaust passages of internal combustion engines for purifying gas components including HC (hydrocarbon), NOx (nitrogen oxides), etc. contained in the exhaust gas emitted from the internal combustion engines. There have been proposed techniques of controlling the air-fuel ratio of an air-fuel mixture to be combusted by an internal combustion engine in order to maximize the purification rate at which gas components such as HC, NOx are purified by the catalytic converter.
For example, the applicant of the present application has proposed a system for achieving an optimum exhaust gas purifying capability of a catalytic converter by sequentially determining a target value for the air-fuel ratio of an exhaust gas upstream of the catalytic converter according to a feedback control process in order to converge an output (detected value of oxygen concentration) of an O2 sensor (oxygen concentration sensor) disposed downstream of the catalytic converter to a predetermined target value (constant value), and manipulating the air-fuel ratio of an air-fuel mixture to be combusted by an internal combustion engine to equalize the air-fuel ratio of the exhaust gas upstream of the catalytic converter with the target air-fuel ratio. See, for example, Japanese laid-open patent publication No. 9-324681 and U.S. Pat. No. 5,852,930, for details. The air-fuel ratio of the exhaust gas upstream of the catalytic converter specifically represents the air-fuel ratio recognized from the oxygen concentration of the exhaust gas that enters the catalytic converter, i.e., the air-fuel ratio of the air-fuel mixture which has been combusted by the internal combustion engine to produce the exhaust gas. This air-fuel ratio will hereinafter be referred to as the air-fuel ratio of the internal combustion engine.
By controlling the air-fuel ratio of the internal combustion engine at an air-fuel ratio state to converge (set) the output of the O2 sensor disposed downstream of the catalytic converter to the predetermined target value, it is possible to achieve the optimum capability of the catalytic converter to purify HC, NOx, etc., i.e., the purifying capability to maximize the purification rate of HC, NOx, etc., irrespective of the deteriorated state of the catalytic converter.
In recent years, there have been developed exhaust gas sensors, specifically HC sensors and NOx sensors, capable of detecting relatively accurately the concentrations of various gas components, including HC, NOx, etc., to be purified by catalytic converters. Some of these exhaust gas sensors generally have their output levels increasing substantially linearly as the concentrations of the detected gas components increase. The output levels of other exhaust gas sensors decrease as the concentrations of the detected gas components increase. The output characteristics of the exhaust gas sensors of the former type will hereinafter be referred to as positive characteristics, and the output characteristics of the exhaust gas sensors of the latter type will hereinafter be referred to as negative characteristics.
If such exhaust gas sensors are used, then it may be possible to control the purification of a gas component by a catalytic converter at a desired state while the concentration of the gas component purified by the catalytic converter is being observed.
For example, such an exhaust gas sensor may be disposed downstream of the catalytic converter, and a target air-fuel ratio for the internal combustion engine may be determined in order to equalize the output of the exhaust gas sensor or the concentration of the gas component recognized from the output of the exhaust gas sensor, i.e., the detected value of the concentration, with a desired value, and the air-fuel ratio of the air-fuel mixture combusted by the internal combustion engine may be controlled based on the target air-fuel ratio.
According to the inventor""s finding, however, the purification rate of a gas component such as HC, NOx, etc. by the catalytic converter is basically maximum when the air-fuel ratio of the internal combustion engine is of a certain value, basically a value near a stoichiometric air-fuel ratio, and is reduced when the air-fuel ratio of the internal combustion engine is shifted into an air-fuel ratio range that is either leaner or richer than that certain value of the air-fuel ratio. Therefore, the concentration of the gas component recognized from the output of the exhaust gas sensor disposed downstream of the catalytic converter has a minimum value as the air-fuel ratio of the internal combustion engine changes. The output of the exhaust gas sensor which has the positive characteristics has a minimum value as the air-fuel ratio of the internal combustion engine changes, and the output of the exhaust gas sensor which has the negative characteristics has a maximum value as the air-fuel ratio of the internal combustion engine changes.
When the output of the exhaust gas sensor or the concentration of the gas component recognized from the output of the exhaust gas sensor differs from a desired value, it is difficult to identify which of the leaner and richer air-fuel ratio ranges the air-fuel ratio of the internal combustion engine should be changed into in order to eliminate the difference. Therefore, it is difficult according to the conventional feedback control process which employs the O2 sensor disposed downstream of the catalytic converter to determine a target air-fuel ratio for controlling the output of the exhaust gas sensor at the desired value.
There has been a demand for a new technique of controlling, at a desired value, the output of an exhaust gas sensor that is disposed downstream of a catalytic converter, for detecting the concentration of a gas component to be purified by the catalytic converter, such as HC, NOx, etc.
It is therefore an object of the present invention to provide an apparatus for controlling the air-fuel ratio of an internal combustion engine to control, well at a desired value, the output of an exhaust gas sensor that is disposed downstream of a catalytic converter, for detecting the concentration of a gas component to be purified by the catalytic converter, such as HC, NOx, etc., or the concentration of the gas component recognized from the output of the exhaust gas sensor.
To accomplish the above object, there is provided in accordance with the present invention an apparatus for controlling the air-fuel ratio of an internal combustion engine, comprising an exhaust gas sensor for detecting the concentration of a particular component in an exhaust gas purified by a catalytic converter which is disposed in an exhaust passage of the internal combustion engine, the exhaust gas sensor being disposed downstream of the catalytic converter, identifying means for identifying the values of parameters of a nonlinear function representing correlating characteristics of the detected concentration of the particular component with respect to an air-fuel ratio of the particular component upstream of the catalytic converter, using data representing the air-fuel ratio of the exhaust gas upstream of the catalytic converter and output data of the exhaust gas sensor, target air-fuel ratio calculating means for determining the value of an air-fuel ratio at which the concentration of the particular component that is represented by a function value of the nonlinear function whose parameters are identified by the identifying means is of a value satisfying a predetermined condition, using the identified values of the parameters of the non-linear function, and obtaining the determined value of the air-fuel ratio as a target air-fuel ratio for the exhaust gas upstream of the catalytic converter, and air-fuel ratio manipulating means for manipulating the air-fuel ratio of an air-fuel mixture combusted by the internal combustion engine depending on the target air-fuel ratio determined by the target air-fuel ratio calculating means.
The nonlinear function has an independent variable represented by data which indicates the air-fuel ratio of the exhaust gas upstream of the catalytic converter, e.g., the output of a sensor-for detecting the air-fuel ratio, the air-fuel ratio recognized from the output of the sensor, or a target value of the air-fuel ratio, and a dependent variable represented by the output of the exhaust gas sensor or the concentration of the particular component recognized from the output of the exhaust gas sensor. The nonlinear function preferably comprises a function of higher degree, e.g., a quadratic function or a cubic function. The parameters are specifically parameters which define the shape of a graphic configuration of the nonlinear function. For example, if the nonlinear function comprises a function of higher degree, e.g., a quadratic function or a cubic function, then the coefficients of terms of various degrees and the constant term of the function serve as the parameters.
The air-fuel ratio of the exhaust gas upstream of the catalytic converter specifically comprises the air-fuel ratio recognized from the concentration of oxygen in the exhaust gas. The air-fuel ratio will sometimes be referred to as the air-fuel ratio of the internal combustion engine.
The identifying means identifies the values of parameters of the nonlinear function using data representing the air-fuel ratio of the internal combustion engine and output data of the exhaust gas sensor, i.e., data of the detected concentration of the particular component. In this manner, the nonlinear function is determined which approximately expresses, with an equation, the correlating characteristics of the detected concentration of the particular component with respect to the air-fuel ratio of the internal combustion engine, i.e., the graphic configuration of the nonlinear function is determined.
Generally, the concentration of the particular component detected by the exhaust gas sensor, i.e., the concentration of the particular component purified by the catalytic converter, has a minimum value as the air-fuel ratio of the internal combustion engine changes. The above correlating characteristics can properly be expressed by a nonlinear function of a suitable type, e.g., a quadratic function or a cubic function.
When the values of the parameters are thus identified to determine the nonlinear function representative of the correlating characteristics, it is possible to calculate, using the identified values of the parameters of the nonlinear function, the value of the air-fuel ratio of the internal combustion engine (the value of the independent variable of the nonlinear function) at which the concentration of the particular component represented by the function value of the nonlinear function (the value of the dependent variable) is of a value (desired value) satisfying a predetermined condition. Since the nonlinear function approximately expresses the correlating characteristics, the calculated value of the air-fuel ratio is capable of controlling the actual concentration of the particular component detected by the exhaust gas sensor at the above desired value.
The target air-fuel ratio calculating means determines the value of the air-fuel ratio at which the concentration of the particular component that is represented by the function value of the nonlinear function is of the value satisfying the predetermined condition, using the identified values of the parameters of the nonlinear function, and obtains the determined value of the air-fuel ratio as the target air-fuel ratio for the internal combustion engine, i.e., the target value of the air-fuel ratio of the exhaust gas upstream of the catalytic converter. The air-fuel ratio manipulating means manipulates the air-fuel ratio of the air-fuel mixture combusted by the internal combustion engine depending on the target air-fuel ratio determined by the target air-fuel ratio calculating means. In this fashion, the air-fuel ratio of the internal combustion engine is manipulated to equalize the concentration of the particular component detected by the exhaust gas sensor with the value satisfying the predetermined condition, i.e., to equalize the output of the exhaust sensor or the concentration (detected value of the concentration) of the particular component recognized from the output of the exhaust sensor with the desired value.
Therefore, the output of the exhaust sensor disposed downstream of the catalytic converter or the concentration of the particular component recognized from the output of the exhaust sensor can well be controlled at the desired value.
The particular component whose concentration is detected by the exhaust gas sensor is specifically HC (hydrocarbon), NOx (nitrogen oxide), or the like.
The data representing the air-fuel ratio of the internal combustion engine, i.e., the air-fuel ratio of the exhaust gas upstream of the catalytic converter, which is used by the identifying means to identify the values of the parameters of the nonlinear function, may comprise data representing the air-fuel ratio itself, but should preferably comprise data representing the difference between the air-fuel ratio of the internal combustion engine and a predetermined reference value.
Using the data representing the difference between the air-fuel ratio of the internal combustion engine and the predetermined reference value, the identified values of the parameters of the nonlinear function are of increased accuracy.
For the identifying means to identify the values of the parameters of the nonlinear function, the target air-fuel ratio determined by the target air-fuel ratio calculating means may be used as the air-fuel ratio of the internal combustion engine. Preferably, however, an air-fuel ratio sensor is disposed upstream of the catalytic converter, for detecting the air-fuel ratio of the exhaust gas upstream of the catalytic converter, and the identifying means may comprise means for identifying the values of the parameters of the nonlinear function using the air-fuel ratio detected by the air-fuel ratio sensor as the air-fuel ratio of the internal combustion engine.
Using the air-fuel ratio detected by the air-fuel ratio sensor, i.e., the actual value of the air-fuel ratio of the internal combustion engine, i.e., the air-fuel ratio of the exhaust gas upstream of the catalytic converter, the values of the parameters of the nonlinear function can be identified with high accuracy.
The air-fuel ratio manipulating means may comprise means for manipulating the air-fuel ratio of the air-fuel mixture combusted by the internal combustion engine according to a feedback control process for converging the air-fuel ratio detected by the air-fuel ratio sensor to the target air-fuel ratio determined by the target air-fuel ratio calculating means.
It is thus possible to control the air-fuel ratio of the internal combustion engine properly at the target air-fuel ratio, and control the output of the exhaust gas sensor accurately at the desired value. As a result, the catalytic converter can reliably maintain its desired purifying capability for purifying the particular component.
The air-fuel ratio of the internal combustion engine should preferably be manipulated according to the feedback control process by a recursive-type feedback control means such as an adaptive controller. The recursive-type feedback control means determines a new feedback controlled quantity according to a given recursive formula containing a predetermined number of time-series data, prior to the present time, of the feedback controlled quantity of the air-fuel ratio, e.g., a corrective quantity for the amount of supplied fuel.
The target air-fuel ratio calculating means preferably comprise means for determining, as the target air-fuel ratio, the value of an air-fuel ratio at which the concentration of the particular component represented by the function value of the nonlinear function is of a minimum value.
The target air-fuel ratio serves to minimize the concentration of the particular component detected by the exhaust gas sensor, i.e., the concentration of the particular component that has been purified by the catalytic converter. When the air-fuel ratio of the air-fuel mixture combusted by the internal combustion engine is manipulated depending on the target air-fuel ratio, the air-fuel ratio of the internal combustion engine is controlled at an air-fuel ratio state in which the purification rate of the particular component by the catalytic converter is maximum. Thus, the particular component can be optimally purified by the catalytic converter in a manner to maximize the purification rate thereof. Stated otherwise, the ability of the catalytic converter to purify the particular component is maximized.
If the dependent variable of the nonlinear function is represented by the concentration of the particular component recognized from the output of the exhaust gas sensor, then the target air-fuel ratio is of a value that minimizes the function value itself of the nonlinear function. If the dependent variable of the nonlinear function is represented by the output of the exhaust gas sensor, and also if the characteristics of the output of the exhaust gas sensor with respect to the concentration of the particular component are positive, i.e., the characteristics are such that the output of the exhaust gas sensor increases as the concentration of the particular component increases, then the target air-fuel ratio is of a value that minimizes the function value itself of the nonlinear function. If the dependent variable of the nonlinear function is represented by the output of the exhaust gas sensor, and also if the characteristics of the output of the exhaust gas sensor with respect to the concentration of the particular component are negative, i.e., the characteristics are such that the output of the exhaust gas sensor decreases as the concentration of the particular component increases, then the concentration of the particular component represented by the function value of the nonlinear function decreases as the function value is greater. Therefore, the target air-fuel ratio is of a value that maximizes the function value itself of the nonlinear function.
Depending on the deteriorated state of the catalytic converter, the concentration of the particular component detected by the exhaust gas sensor may not have a minimum value as the air-fuel ratio of the internal combustion engine changes. For example, as described in detail later on, if the particular component is HC or NOx and the catalytic converter such as a three-way catalytic converter is brand-new, then when the air-fuel ratio of the internal combustion engine is in an air-fuel ratio range leaner or richer than a certain air-fuel ratio, the concentration of HC or NOx detected by the exhaust gas sensor, i.e., an HC sensor or an NOx sensor, is substantially constant, and does not have a minimum value.
In this case, the value of the air-fuel ratio at which the concentration of the particular component represented by the function value of the nonlinear function determined by the identifying means is of a minimum value, i.e., the target air-fuel ratio, may often be inappropriate or excessively lean or rich in purifying other gas components, though it may not pose problems for the catalytic converter to purify the particular component. If the actual concentration of the particular component detected by the exhaust gas sensor does not have a minimum value, then the minimum value of the concentration of the particular component represented by the function value of the nonlinear function cannot generally be employed in reality as representing the concentration detected by the exhaust gas sensor.
According to the present invention, the target air-fuel ratio calculating means comprises means for, if the minimum value of the concentration of the particular component represented by the function value of the nonlinear function falls out of a predetermined range, determining the value of an air-fuel ratio at which the concentration of the particular component represented by the function value of the nonlinear function is of a predetermined value, using the identified values of the parameters of the nonlinear function, and obtaining the determined value of the air-fuel ratio as the target air-fuel ratio, instead of determining, as the target air-fuel ratio, the value of the air-fuel ratio at which the concentration of the particular component represented by the function value of the nonlinear function is of the minimum value.
With the above arrangement, even in a situation where the concentration of the particular component detected by the exhaust gas sensor does not have a minimum value as the air-fuel ratio of the internal combustion engine changes, it is possible to determine a target air-fuel ratio for allowing the catalytic converter to well purify various gas components including the particular component. In a situation where the concentration of the particular component detected by the exhaust gas sensor has a minimum value, if the minimum value of the concentration of the particular component represented by the function value of the nonlinear function is an inappropriate value falling out of a predetermined range due to a disturbance, then it is possible to avoid the determination of a target air-fuel ratio that is not suitable for the catalytic converter to purify various gas components.
The parameters of the nonlinear function may be identified after the data of the air-fuel ratio sensor and the exhaust gas sensor have been collected and accumulated. However, the identifying means comprises means for sequentially identifying the values of the parameters of the nonlinear function according to a sequential identifying algorithm.
Since the sequential identifying algorithm is used, a memory capacity required to execute the sequential identifying algorithm may be small. Because the parameters of the nonlinear function are sequentially updated on a real-time basis to determine the nonlinear function, it is possible to sequentially determine the target air-fuel ratio depending on behavioral states of the catalytic converter and the internal combustion engine from instant to instant. As a result, the output of the exhaust gas sensor or the concentration of the particular component recognized from the output of the exhaust gas sensor can be controlled at the desired value with an increased response.
The sequential identifying algorithm may comprise any one of the algorithms of a sequential method of least squares, a sequential method of weighted least squares, a fixed gain method, a degressive gain method, etc. According to these algorithms, new values of the parameters are determined, i.e., the values of the parameters are updated, in order to minimize an error or difference between the value of the output of the exhaust gas sensor determined according to the nonlinear function using the present identified values of the parameters and the actual value of the output of the exhaust gas sensor.
In the present invention for the identifying means to use the sequential identifying algorithm, the identifying means preferably comprise means for identifying the values of the parameters of the nonlinear function while limiting at least one of the parameters to a value satisfying a predetermined condition.
Specifically, the parameters of the nonlinear function whose values are identified by the identifying means include such a parameter that if the value thereof is erroneously identified as a value falling out of a certain desired range due to disturbances or the like, the actual configuration of the graph of the correlating characteristics becomes largely different from the configuration of the graph of the nonlinear function. According to the present invention, when at least one of the parameters of the nonlinear function is to be identified, the value of the parameter is limited to a value which satisfies a certain condition. In this manner, the value of the parameter is prevented from being identified in error, and the nonlinear function representing the correlating characteristics is made reliable. As a consequence, the reliability of the target air-fuel ratio determined using the nonlinear function is increased
If the nonlinear function comprises a quadratic function, then the identifying means comprises means for using the coefficient of a term of maximum degree of the quadratic function as the one of the parameters which is limited to the value, and limiting and identifying the value of the coefficient such that the concentration of the particular component represented by the function value of the quadratic function has a minimum value.
Specifically, the function value of the quadratic function has a minimum value or a maximum value depending on whether the coefficient of the term of maximum degree is positive or negative. If the identified value of the coefficient is of an inappropriate sign, i.e., positive or negative sign, then the concentration of the particular component represented by the function value of the quadratic function as the nonlinear function has a maximum value rather than a minimum value that it should have. For this reason, the identified value of the coefficient is limited so that the concentration of the particular component represented by the function value of the quadratic function has a minimum value. Specifically, the identified value of the coefficient is limited to a positive or negative value. In this manner, a basic match between the quadratic function as the nonlinear function representing the correlating characteristics and the correlating characteristics is reliably achieved.
More specifically, if the dependent variable of the quadratic function as the nonlinear function is represented by the concentration of the particular component recognized from the output of the exhaust gas sensor or the output of the exhaust gas sensor of positive characteristics, then the coefficient of the term of maximum degree of the quadratic function is limited to a positive value. If the dependent variable of the quadratic function is represented by the output of the exhaust gas sensor of negative characteristics, then the coefficient of the term of maximum degree of the quadratic function is limited to a negative value.
If the nonlinear function comprises a cubic function, then the identifying means comprises means for using the coefficient of a term of maximum degree of the cubic function as the one of the parameters which is limited to the value, and limiting and identifying the value of the coefficient such that the gradient of the graph of the cubic function in air-fuel ratio ranges on both sides of the value of an air-fuel ratio at which the concentration of the particular component represented by the function value of the cubic function has a minimum value, has a predetermined shape depending on the type of the particular component.
In the graph of the actual correlating characteristics of the concentration of the particular component detected by the exhaust gas sensor with respect to the air-fuel ratio of the internal combustion engine, the graph may have different gradients, i.e., the concentration of the particular component may change differently as the air-fuel ratio changes, in the air-fuel ratio ranges leaner and richer than the value of the air-fuel ratio at which the concentration of the particular component is of a minimum value, depending on the type of the particular component. The cubic function as the nonlinear function can have both maximum and minimum values irrespective of whether the coefficient of the term of maximum degree thereof is of a positive value or a negative value. However, the pattern of changes of the graph of the cubic function in the air-fuel ratio ranges on opposite sides of the air-fuel ratios corresponding to those extremal values differs depending on whether the coefficient of the term of maximum degree (third degree) thereof is of a positive value or a negative value.
The identified value of the coefficient is limited, i.e., it is limited to a positive value or a negative value, in order that the gradient of the graph of the cubic function in the air-fuel ratio ranges on opposite sides of the value of the air-fuel ratio at which the concentration of the particular component represented by the function value of the cubic function as the nonlinear function is of a minimum value is of a predetermined shape.
In this fashion, a match between the actual correlating characteristics and the cubic function as the nonlinear function is reliably achieved.
If the gradient of the graph of the correlating characteristics differs in the air-fuel ratio ranges that leaner and richer than the value of the air-fuel ratio at which the concentration of the particular component is of a minimum value, then the cubic function is preferable to the quadratic function as the nonlinear function for increasing the match between the nonlinear function and the correlating characteristics.